What are the solutions to the equation 4x^2-36x=-69 ?

The solutions to the equation 4x^2-36x=-69 are x=(9+2sqrt(3))/2 ,x=(9-2sqrt(3))/2

Find the zeros of 4x^2-36x=-69

The zeros of 4x^2-36x=-69 are x=(9+2sqrt(3))/2 ,x=(9-2sqrt(3))/2

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4 x^{2} - 36 x = - 69

x = \frac{9 + 2 3}{2}, x = \frac{9 - 2 3}{2}

Decimal Notation

x = 6.23205 \dots, x = 2.76794 \dots

Solution steps

4 x^{2} - 36 x = - 69

Move

69

to the left side

4 x^{2} - 36 x + 69 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 36 ) \pm ( - 36 ) ^{2} - 4 \cdot 4 \cdot 69}{2 \cdot 4}

(- 36)^{2} - 4 \cdot 4 \cdot 69 = 83

x_{1, 2} = \frac{- ( - 36 ) \pm 8 3}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 36 ) + 8 3}{2 \cdot 4}, x_{2} = \frac{- ( - 36 ) - 8 3}{2 \cdot 4}

x = \frac{- ( - 36 ) + 8 3}{2 \cdot 4} : \frac{9 + 2 3}{2}

x = \frac{- ( - 36 ) - 8 3}{2 \cdot 4} : \frac{9 - 2 3}{2}

The solutions to the quadratic equation are:

x = \frac{9 + 2 3}{2}, x = \frac{9 - 2 3}{2}

10 x^{2} - 8 x - 8 = 0

4 x^{2} + 61 = 28 x

4 x^{2} + 69 = 36 x

6 (x - 3)^{2} - 6 = 0

y, x^{2} + 2 x y + y^{2} = 0

What are the solutions to the equation 4x^2-36x=-69 ?
The solutions to the equation 4x^2-36x=-69 are x=(9+2sqrt(3))/2 ,x=(9-2sqrt(3))/2
Find the zeros of 4x^2-36x=-69
The zeros of 4x^2-36x=-69 are x=(9+2sqrt(3))/2 ,x=(9-2sqrt(3))/2